My first real job interview was at SIG, one of the world's leading market making firms. I got asked the following interview question. Follow along and see how you would do. /1

2/ The interviewer asked me for a 90% confidential interval on the population of France. (i.e. a low estimate and a high estimate of population, that I'm 90% confident the correct answer falls in between). (this is just the first step, they don't care about my geographic skill)

3/ I reasoned that I know France is far smaller than the US (population ~300 million at the time), and I was virtually certain that it was substantially larger than New York City (~8 million). I vaguely remembered reading that it had a population of about 50 million.

4/ so, my 90% confidence interval was 30 million at 100 million. I expected to be wrong 10% of the time if I made a series of similar guesses about other countries. Again - they don't care about geographic knowledge, this is the warm up.

5/ Then the interviewer offered to bet me $1 of real money that I was wrong. She was betting that the correct population was either >100 million or <30 million. Would I take that bet? If I take the bet and am wrong, I lose $1.

6/ my answer: yes, I'll take the bet. I was 90% confident in my estimate, and your willingness to bet me $1 makes me a little less confident, but still more than 50% confident. Okay she says, "how about we bet $100, and FYI, I'm making this bet personally with my own money."

7/ my answer: I'll take the bet, but barely. Your willingness to bet $100 suggests you know something that I don't. Maybe you just googled the population of France. Maybe a nuclear bomb just went off wiping France off the map and you know this but I don't. But...

8/ the contrived nature of the bet (as part of an interview) makes me think you would offer to bet against me regardless of your knowledge to test my reaction, and the $100 stakes are small enough that you would willingly lose that for the sake of the interview.

9/ that was the end - they liked the answer - that I realized that the fact that she was willing to bet against me meant I needed to "update" my confidence. I was 90% confident at the start, but someone eager to bet against me is new information.

10/ for interviewees who happily accepted the $100 bet with no justification, or by sticking to their 90% confidence, the next step is the interviewer would grab a colleague who would excitedly rush in and say they too wanted to bet against the interviewee for larger sums.

11/ if the interviewee still says they want to bet because their confidence is unshaken in their original 90% confidence interval, they don't get the job. It suggests they don't understand that the bets represent new information.

12/ poker players naturally do well with this type of question (and often make good traders), because we're used to having to update our estimates. If you're dealt QQ in a 10-person game, you know you likely have the best hand. But if a conservative player raises and re-reraises

13/ we realize that our odds of having the best hand has fallen substantially, maybe far below 50%. In contrast, engineers often struggle with this type of question because they're used to being taught a "correct" equation or model and being confident in the result.

14/ I hope I'm not breaching etiquette in revealing an interview question with a former employer given that the interview was 15 years ago....

15/ a truism from the gambling world: "son, someday a man is going to offer you a bet in a bar. He'll offer to bet you $1,000 that a jack of spades is gonna jump up out of a deck and spit cider in your ear. If you take that bet...sure enough you're gonna have a wet ear."